Thermal stress in thick walled cylinder

[NovaStark]

I am trying to approximate the stresses due to temperature and pressure in a thick walled cylinder. I attached the results of the calculation however, I suspect my formulas that I am using are incorrect.

I derived them by using the basic elastic theory equations. However as it can be seen, my axial stress is overly high so I am not sure if I am using the correct equations. Can anyone point me to the correct direction to get the proper equations or see what I am doing wrong in my calculation? I am trying to get API 530 to see what they use for stresses.

 

[davefitz]

Successful designs of this type always allow one of the headers to freely float, ensuring zero thermal axial thermal stress. In the case of a large boiler ( say, a 1200 MWe / 3600 MWth coal fired boiler)the tubes and piping are top supported , and the bottom headers are free to mover downward with the increase in length dur to thermal growth. This growth can be as much as 0.3 m. 12 " downward growth.

"Nobody expects the Spanish Inquisition! "

 

[chicopee]

Based on your attachment data on tube size, the equipment has thin wall tubing as I am basing thin wall thickness at or less than 1/20th of internal diameter of the tubes.

 

[NovaStark]

Based on your attachment data on tube size, the equipment has thin wall tubing as I am basing thin wall thickness at or less than 1/20th of internal diameter of the tubes.

The part of the tube experiencing the downward firing is 1/2 inch thick with an ID of 4.22 inches gives 0.118 which is more than 1/20 (0.05), so it is thick?

 

[chicopee]

If tube thickness is less than 1/20 th internal diameter, it is thin wall tubing.

 

[NovaStark]

If tube thickness is less than 1/20 th internal diameter, it is thin wall tubing.

So using thick wall equations would be correct. Are there any official standards that state 1/20th of the ID is to be used as thin/thick walled?

 

[desertfox]

Hi Novastark

I am led to believe that the thick walled cylinder formula's are good for both thick and thin walled tube, the thin walled tube formula just simplifies the calculation by assuming the hoop stress is constant throughout.

desertfox

 

[NovaStark]

Ah thank you then. Now that I think about it, it does make sense for it to be applicable to both!

 

[corus]

If you're using thin wall assumptions in Finite Elements or other calculations then the stress through the wall thickness is assumed to be linear, ie. you won't calculate any peak stresses due to features but should calculate the membrane plus bending for assessment against design codes. My approximate formula for thermal stresses in a thin wall gave a value of 119 MPa, whereas the correct analytical approach gave a value of 127 MPa. That should give you some confidence on how appropriate a thin wall assumption is in this case.